Re-visiting the relationship between net ecosystem carbon balance (NECB) and the depth to the water table – a case of Simpson paradox?

A relationship between the net ecosystem carbon balance (NECB) and the depth to water table (WTD) has been commonly quoted and used to justify restoration (Evans et al. (2021). However, there are some curious aspects to this relationship. Firstly, the relationship is linear over all depths which implies that the link between the carbon losses and water table is constant, i.e. if the water table in a peat declines then the impact is the same at 10 cm depth as it is at 75 cm depth. A constant susceptibility to degradation with depth in the peat profile would not fit with our understanding of peat accumulation. Secondly, the relationship has no significant fit for peatlands which are reported as net sinks – it only works for net sources. Tiemeyer et al. (2021) provided an alternative relationship based upon a Gompertz function where a linear relationship becomes a constant value at the extremes of water table depth. So in this study we expanded the available dataset and used Bayesian hierarchical modelling with the available factorial and covariate information to re-assess the link between NECB and depth to the water table. Within the hierarchical modelling both linearizable and non-linearizable relationships were considered. The data were considered by global peatland type (boreal, temperate and tropical) and the temperate peatlands  were also considered separately by sub-type (cropland, drained, grassland, natural and rewetted). There were 752 studies that we could consider – 447 studies of temperate peatlands.

Our study shows that:

• NECB of boreal and temperate peatlands were not significantly different from each other, or from zero, but tropical peatlands were significant sources.
• NECB of natural, rewetted and drained sub-types were not significantly different from each other, but cropland and grassland sub-types were significantly different from all other sub-types.
• By global type there were significant relationships with depth to water table for temperate and tropical peatlands but not for boreal peatlands, and the slopes were not significantly different between tropical and temperate.
• There is little evidence that a linear relationship between NECB with WTD exists: previous published versions of the relationship were dominated by results from grasslands which are generally drier and larger sources than other settings, but within grasslands there is no relationship.
• Where a relationship does exist, then a Gompertz function solves some of the interpretation problems of a linear relationship. Although the Gompertz function itself has a linear portion.
• All relationships fitted poorly for sinks.

The study shows that Simpsons paradox may govern the apparent relationship between NECB and water table and that once a suitable grouping factor is applied any relationship breaks down: the use of non-linear relationships does not resolve the problem.

This finding has important implications for the management of peatlands and shows that a relationship between NECB and WTD is not common – what does that mean for our understanding of peatland accumulation and degradation? Further, if not WTD as a control then what are the common drivers on NECB?

Evans et al. (2021).  Nature, 593(7860), 548–552.

Tiemeyer et al. (2021). . Global Change Biology, 22(12), 4134–4149.